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This article explores a wide range of envelope soliton pulses and their behavior during propagation through a birefringent optical fiber. The propagation of light in such fibers is governed by two coupled non-linear Schrödinger equations (CNLSEs), which account for both coherent and incoherent non-linear couplings. To investigate these solitons, an improved modified extended tanh function scheme (IMETFS) is employed. The study focuses on elliptical core optical fibers and examines the significance of various optical solitons in the presence of group-velocity dispersion and third-order nonlinearity. The findings illustrate that birefringent optical fibers can generate a diverse array of nonlinear periodic waves and localized pulses. The different types of soliton solutions identified include singular, bright, rational, exponential, Jacobi elliptic functions (JEFs), Weierstrass elliptic doubly periodic solutions, and singular periodic solutions. Comparisons with existing literature highlight the novelty and substantive contributions of the discovered wave solutions to current research in nonlinear optics. The success of this approach suggests its potential applicability in addressing nonlinear challenges across different fields, particularly in soliton theory, where similar models are frequently encountered. Additionally, the article presents visual representations of these solutions through 3D and 2D plots, aiding in the understanding of their behaviors. [ABSTRACT FROM AUTHOR]

In this paper, the analytical solutions of the complex coupled Higgs field equation, which explains a system of conserved scalar nucleons that interact with neutral scalar mesons in particle physics, are extracted. The enhanced modified extended tanh expansion method (eMETEM) is successfully employed to solve the considered equation. Besides, the effect of problem parameters on a real scalar meson field and a complex scalar nucleon field is investigated, plotted and interpreted. Some effective results are obtained in the examination and are presented for the first time in this study. The obtained results can be applied to a wide range of nonlinear equations including ocean and shallow-water waves. 3D, 2D and contour graphical representations of the attained solutions are given using appropriate parameters. The method is efficient for gathering analytical solutions for various kinds of phenomena modeling by classical, fractional, or stochastic partial differential equations. [ABSTRACT FROM AUTHOR]

This study examines the analytic wave solutions of a highly dispersive perturbed complex Ginzburg–Landau equation (CGLE) with conformable fractional derivative and polynomial law of nonlinearity using the improved modified extended tanh-function method. The results show a wide range of solutions including (bright, dark, singular) solitons, Jacobi elliptic solutions, exponential solutions, and Weierstrass elliptic solutions. The obtained soliton solutions showcase diverse dynamics, encompassing different solitary waves and localized structures. The polynomial nonlinearity adds complexity to the dynamics, resulting in the emergence of new solitons with distinct characteristics. The impact of the fractional derivative is illustrated graphically using examples of some of the retrieved solutions with various values of fractional order. [ABSTRACT FROM AUTHOR]

The Biswas–Mollivic equation is a special type of nonlinear Schrödinger equation, which explains the spatio-temporal behaviour of excitable media. In this paper, we investigate the optical soliton solutions of the Biswas–Mollivic equation with cubic–quintic–septic–nonic nonlinearities using the generalized Riccati equation mapping method. This method is efficient and provides new perspectives. It also provides novel insights into the dynamics of excitable media. Our findings add to a better understanding of the complex spatio-temporal patterns that develop in excitable media and have potential applications in the design of new technologies for controlling and manipulating pattern formation. To depict optical soliton solutions graphically, we use the MATLAB software. [ABSTRACT FROM AUTHOR]

This paper examines the complex Ginzburg Landau equation, which describes pulse propagation inside a fiber with the triple power law of self-phase modulation. Since the effect of parameter selection has become very important in relevant model studies recently, self-phase modulation has been added to the complex Ginzburg Landau equation, which has been studied in the literature, and it is aimed at investigating the analytical solutions of the presented equation. Adding the triple power law of the self-phase modulation parameter to the model, in addition to existing studies in the literature, emphasizes the innovative aspect and importance of the study. The first aim is to reveal bright and singular solitons using the new Kudryashov method. The new Kudryashov method is a technique that is frequently used in the literature, is effective for generating analytical solutions, provides ease of operation, and can be applied to a wide class of nonlinear partial differential equations. The second goal is to show that the obtained solutions have modulation stability. By using modulation instability analysis, the gain spectrum is formed for different parameter values. Graphic presentations support the findings. Moreover, bright and singular soliton portraits are demonstrated with 3D and 2D graphs. The novelty of the study lies in the fact that the relevant model has not been studied before with an effective method such as the new Kudryashov method, and the modulation instability has been studied for the first time. [ABSTRACT FROM AUTHOR]

Studying the highly dispersive model with arbitrary refractive index initiated by Kudryashov is the subject of this work. This model depicts the behavior of soliton propagation via polarization-preserving fibers. To secure a dark soliton and like-solitons with singularities solution for the proposed model, the generalized Kudryashov's integration approach has been utilized. This method do not have any constraints on how to find solutions. Some significant solutions have been graphically elaborated in the form of 2D and 3D plots by selecting the appropriate parameters to provide a better physical illustration and understanding of the dynamical physical properties of this model. [ABSTRACT FROM AUTHOR]

In this work, we take into account the (2+1)-Davey Stewartson equation (DSE) and the (2+1)-complex coupled Maccari system (CCMS) and their analytical solutions. Besides, we tackle the role of the problem parameters on the soliton behavior produced by the presented DSE. Exact traveling wave solutions are highly useful in numerical and analytical theories for such equations. While numerical methods are widely used, improving analytical approaches for obtaining analytical solutions is necessary for a deeper understanding of dynamics. This study marks a significant milestone by implementing the efficient analytical approach, enhanced modified extended tanh expansion method, for the first time to the (2+1)-DSE and (2+1)-CCMS equations, thereby making a notable contribution to the existing literature. We have shown that features of the soliton solutions can represent the spread of propagation on the wavefronts and show a reasonable dependency on parameter values. Some of the solutions discovered in three- and two-dimensional arrangements can also be described in graphic representations of their behavior. With the help of the graphical depictions, bright, singular, and periodic singular soliton characters for the (2 + 1) -DSE and singular, dark, bright, and periodic singular soliton characters for the (2 + 1) -CCMS are acquired. The results show that the utilized analytical technique is easily applicable, efficient, reliable, robust, and categorical when it comes to finding analytical solutions for different nonlinear models. Moreover, the problem parameters and the coupling coefficients have significant influences on the behavior of the solitons of the DSE, and this examination is studied for the first time in this article. [ABSTRACT FROM AUTHOR]

This article investigates the dynamics of optical solitons in a magneto-optic waveguide with the nonlinear perturbed Schrödinger equation. The model incorporates two generalized nonlocal laws, a Kudryashov's sextic-power law nonlinear structure, and high dispersion up to the sixth-order dispersion. The proposed innovative model ensures that all the obtained solutions are original and have not been reported elsewhere. The impetus for this work is the recognition of the crucial significance of studying nonlinear magneto-optical interactions in optical communication systems. The nonlinear Schrödinger equation and its derivatives play crucial roles in various scientific areas, particularly in the field of nonlinear optics and optical fibers. In order to investigate the new structure of our model, we utilize the Z ′ Z -expansion technique and the enhanced Kudrtashov's method. The solitons obtained are of several types, including bright, singular, and combinations thereof as well as kink-type solution. The strategies utilized are efficacious and distinctive tools in their methodologies and results. To further elucidate the dynamics of the acquired solitons, we offer a discussion section where we present plots of specific solitons. [ABSTRACT FROM AUTHOR]

In this paper, (1 + 1) -dimensional Schrödinger–Hirota equation with Kerr law having inter-modal dispersion is considered. This model designates the propagation of pulses in optical fibers, so it has a significant impact on the model and optimization of optical fiber communication systems. Utilizing the Lie symmetry technique, three generators are produced and three sub-algebras are derived by the combination of these generators. Lie symmetry analysis is the basis of the reduction of the presented nonlinear partial differential equation to the nonlinear ordinary differential equation system. We implement the unified Riccati equation expansion method so that we acquire the analytical soliton solutions. Thus, periodic singular, dark, and singular solitons are retrieved; besides, their 3-dimensional portraits are illustrated by selecting appropriate parameter values. Moreover, the influence of the parameters of the presented model is investigated via various 2-dimensional graphical visualizations. This study reports that all produced solutions satisfy the presented model. [ABSTRACT FROM AUTHOR]

This study centers on examining the characteristics of the recently extended (3 + 1) -dimensional nonlinear equation proposed by Kudryashov. The extended F-expansion technique is employed to derive solitons and other exact wave solutions for this model. Applying this technique results in a diverse set of solutions, encompassing bright solitons, dark solitons, singular solitons, hyperbolic solutions, periodic solutions, singular periodic solutions, exponential solutions, rational solutions, and solutions involving Jacobi elliptic functions (JEF). This method proves to be a dependable and efficient approach for obtaining exact solutions for various nonlinear partial differential equations (NPDE). Visual representations through graphical illustrations are provided to depict the dynamics of selected solutions, and the influence of the parameter n on the obtained solutions is scrutinized and presented in pertinent figures. These discoveries not only advance our comprehension of nonlinear wave phenomena but also hold practical significance for fields related to wave propagation, nonlinear optics, and optical systems. [ABSTRACT FROM AUTHOR]

In this article, we are interested in two principal topics. First, the bright optical soliton solutions of the third-order (1+1)-nonlinear Schrödinger equation including power law nonlinearity with inter-modal and spatio-temporal dispersions are perused by taking advantage of the new Kudryashov method. Second, the impacts of power law nonlinearity parameters on soliton attitude are investigated for acquired bright soliton form. With the proposed technique, the bright optical soliton solution is acquired, and 3D, contour, and 2D plots are depicted. Then, the impact of power law nonlinearity parameters on the soliton attitude has been successfully demonstrated. As is clear from this perusal power law parameters have an important impact on the soliton attitude, and this impact alters based on the soliton form. As regards our investigation, this form of the equation has not been studied with the power law nonlinearity in the absence of the chromatic dispersion for nonlinear models and the proposed method has not been applied the introduced equation before. It is expected that the consequences which are acquired in this study will shed light on the studies in this field. [ABSTRACT FROM AUTHOR]

The mathematical efficiency of fractional-order differential equations in modeling real systems has been established. The first-order and second-order time derivatives are substituted in integer-order problems by a fractional derivative of order 0 < ω ≤ 1 , resulting in time-fractional heat and wave problems with variable coefficients. In this research, we analyze fractional-order wave and heat problems with variable coefficients within the framework of a Caputo derivative (CD) using the Elzaki residual power series method (ERPSM), which is a coupling of the residual power series method (RPSM) and the Elzaki transform (E-T). It relies on a novel form of fractional power series (FPS), which provides a convergent series as a solution. The accuracy and convergence rates have been proven by the relative, absolute, and recurrence error analyses, demonstrating the validity of the recommended approach. By employing the simple limit principle at zero, the ERPSM excels at calculating the coefficients of terms in a FPS, but other well-known approaches such as Adomian decomposition, variational iteration, and homotopy perturbation need integration, while the RPSM needs the derivative, both of which are challenging in fractional contexts. ERPSM is also more effective than various series solution methods due to the avoidance of Adomian's and He's polynomials to solve nonlinear problems. The results obtained using the ERPSM show excellent agreement with the natural transform decomposition method and homotopy analysis transform method, demonstrating that the ERPSM is an effective approach for obtaining the approximate and closed-form solutions of fractional models. We established that our approach for fractional models is accurate and straightforward and researcher can use this approach to solve various problems. [ABSTRACT FROM AUTHOR]

This study examines for the first time the adapted parabolic law nonlinearity form of (2+1)-dimensional Davey-Stewartson system, an important equation modeling the surface water wave packets with finite depth. For the first time, we will investigate the parabolic law nonlinearity form. Not only is this a significant aspect, but we will also explore it with various parameter values to see its impact on soliton dynamics. In order to transform the nonlinear partial differential equation into a form for which the analytical method can be applied, the ordinary differential equation structure obtained by first applying wave transformation. In the following stage, we implement the new Kudryashov method and sinh-Gordon equation expansion techniques to retrieve bright, dark, singular, and different types of kink solitons. The effect of parabolic law nonlinearity parameters on the obtained soliton types has also been examined. We illustrate the 3D and 2D graphs of some of the obtained solutions to gain a physical perspective. The study will contribute to the literature in terms of the form of the examined problem, its content and results, and the effectiveness of the applied methods. [ABSTRACT FROM AUTHOR]

This article delves into the study of the perturbed cubic-quartic Kudryashov's equation having the Kudryashov's law of refractive index which is recently introduced to the literature. Utilizing the extended rational sine/cosine and sinh/cosh methods, optical solutions such as dark, periodic, and singular are successfully extracted. The two- and three-dimensional plots of these solutions are demonstrated. Besides, the behavior of solitons and the effects of parameters on wave properties are vividly illustrated to explore how the model's parameters influence these solutions. The findings herein can serve as a positive contribution to future research in nonlinear optics, while the methodology employed can be leveraged for similar nonlinear models in real life. [ABSTRACT FROM AUTHOR]

For the first time, we intend to scrutinize both the bright optical soliton solutions of the perturbed Schrödinger–Hirota equation with cubic–quintic–septic law having the spatiotemporal dispersion and the influences of the considered equation parameters on the soliton structure. The simple version of the new extended auxiliary equation method is utilized to carry out the aims. Taking the suitable complex wave transformation, the investigated equation becomes a nonlinear ordinary differential equation. Then, a system consisting of equations in polynomial structure utilizing the technique was able to produce. The bright optical solution is generated by utilizing the presented method. Finally, numerous projections of the bright soliton are indicated to explain the propagation of optical pulses in optic fibers. Furthermore, some depictions describing the effect of the model parameter were added. [ABSTRACT FROM AUTHOR]

In this study, for the first time, a study on optical soliton solutions of the stochastic perturbed Schrödinger-Hirota equation which models the propagation of solitons through optical fibers having the Kerr law is carried out. For this purpose, the nonlinear partial differential equation of the examined model is first reduced to the nonlinear ordinary differential equation form using the complex wave transformation. Then, using the new Kudryashov and the Kudryashov methods, bright, dark and singular soliton solutions are derived as a basic step. The next part is devoted to the examination of the noise effect, and first of all, soliton solutions are obtained in the absence of noise strength. Afterwards, the same soliton solutions are obtained, taking into account the noise effect, and comparison and comments are made. In addition to the fact that the form of the examined equation has not been presented and studied before. Considering that, in today's world, taking into account the effect of noise is an inevitably important factor for engineering models to be designed correctly and to operate efficiently, it is obvious that the results obtained will contribute to the literature. [ABSTRACT FROM AUTHOR]

In this study, we investigated Schrödinger–Hirota equation Kerr law in the presence of spatio-temporal dispersion which describes pulse propagation in optical fibers provoked by nonlinear effect and reduced to multi-plane dispersion. We used the Lie symmetry method to reduce the model into the nonlinear ordinary differential equations. Moreover, the unified Riccati equation expansion method was used to obtain optical soliton solutions and other soliton solutions of the model. We obtained dark, kink, singular, and periodic-singular soliton solutions. Obtained results were shown via 3D and contour graphs. Thus, the model was analyzed for the first time with the Lie symmetry method and UREEM. [ABSTRACT FROM AUTHOR]

In this manuscript, the density-dependent space-time fractional reaction–diffusion equation in the sense of conformable and M-truncated derivatives (CMD) is presented. Through fractional transformation, these nonlinear fractional equations can be converted into nonlinear ordinary differential equations (NLPDEs). Besides, with the help of the Riccati–Bernoulli sub-ODE method (RBM), new exact solutions for these nonlinear fractional equations are produced. In order to construct the comparative analysis between different type fractional derivatives, graphical representations are demonstrated for chosen values of unknown parameters. [ABSTRACT FROM AUTHOR]

In this paper, we studied stochastic perturbed nonlinear Schrödinger equation in fibers with Kerr law nonlinearity. The investigated model is important for the optical pulse propagation in fibers. In addition, we introduced the stochastic version of the related model. We have used the F-expansion method to obtain optical soliton solutions. As a result of the implementation, we reached dark, bright, periodic-singular and periodic soliton solutions. Besides all, we have investigated the white noise effect on the obtained results by simulating the graphics. Moreover, we discussed the effects of some parameters by presenting them in 2D views. The strength face of this study are introducing the stochastic model, obtaining its solutions, investigating noise and parameter effects for the first time. [ABSTRACT FROM AUTHOR]

In this paper, for the first time, we investigated the Kerr and parabolic law forms of the dispersive Schrödinger-Hirota equation in the presence of chromatic and inter-modal dispersions via the Sinh-Gordon equation expansion method. We gained dark, bright, kink and singular soliton solutions and we depicted their 3D, 2D, contour views. As an additional investigation, the effect of parameters on the model was examined and various 2D graphical simulations were portrayed. [ABSTRACT FROM AUTHOR]

In this article, we presented and investigated a model of the (2+1)-dimensional Heisenberg ferromagnetic spin chain (HFSC) equation with parabolic law nonlinearity, for the first time. This study intends on two main elements. The first is to construct the parabolic law nonlinearity form of the HFSC model, and the second is to peruse the effect of this form on the soliton wave behavior. Two different analytical techniques, which are a subversion of the new extended auxiliary equation method and the improved generalized Kudryashov method (iGKM), are applicated to construct the soliton solutions of investigated HFSC form. With the help of these methods, bright, singular, and kink soliton forms have been obtained and their characteristics have been depicted by 2D and 3D diagrams. In accordance with our litterateur investigation, the subject of the study and the results obtained have not been reported before and we can say that the results we have attained will be a guide for researchers who want to study in this field. [ABSTRACT FROM AUTHOR]

In this paper, we investigate existence, boundedness, asymptotic behavior and the oscillatory behavior of the positive solutions of the fuzzy difference equation z n + 1 = A + B z n - m 1 + C z n - m 2 , n ∈ N 0 , where (z n) is a sequence of positive fuzzy numbers, A, B, C and the initial values z - j , j = 0 , 1 , ... , s , are positive fuzzy numbers and m 1 , m 2 are nonnegative integers with s = max m 1 , m 2 . By studying this equation, we generalize and improve some results from the literature. [ABSTRACT FROM AUTHOR]

This research article holds two main purposes. The first purpose is obtaining the optical soliton solutions of the (1 + 1) -dimensional dispersive Schrödinger–Hirota equation in the presence of spatio-temporal dispersion with parabolic law nonlinearity. The second is scrutinizing the impact of the parameters. We utilized the new Kudryashov scheme which is the recent effective, efficient, and easily applicable technique. Performing the wave transformation the nonlinear ordinary differential form (NLODF) is gained. Then utilizing the new Kudryashov method the polynomial structure and its solution sets are derived. Selecting the appropriate solution set, establishing the solution function, providing the main equation, linear modulation stability analysis, and graphical presentations in 3D, and 2D are the issues performed in the remaining parts of the article. [ABSTRACT FROM AUTHOR]

This article investigates the optical soliton solutions of the Kundu–Mukherjee–Naskar (KMN) equation with the help of the enhanced modified extended tanh method (eMETEM). The equation is crucial for simulating the bending of light beam, rogue waves in the seas, and fiber pulses in optics. Some different kinds of solitons such as singular-periodic, dark and singular for the KMN equation have been successfully obtained by the used method. Utilizing Maple, we confirm that all acquired solutions satisfy the considered equation. We have also analyzed the impact of the parameters graphically in the considered equation. The results shown in the figures reveal that the parameters of the considered equation have an important effect upon soliton dynamics. It is anticipated that the gained solutions and used approach would create remarkable chances for future work in a variety of science areas. [ABSTRACT FROM AUTHOR]

The aim of this study is to peruse the dispersive Schrödinger–Hirota equation (SH equation) with parabolic law linearity to get optical soliton solutions by utilizing the generalized Kudryashov method (GKM). Firstly, we introduced the solution algorithm of GKM. Then, we substituted the traveling wave transform to dispersive SH equation with parabolic law and gained nonlinear ordinary differential equation (NODE) form of real and imaginary parts. We successfully applied GKM to the NODE form of dispersive SH equation and obtained the appropriate solution sets. Using these sets, the solution of differential equation and necessary transformations, we created the analytical solution functions of dispersive SH equation and demonstrated the graphical simulations. Optical soliton solutions were obtained, graphical representations were made and interpreted, at the same time, it was observed that some parameters had an effect on the soliton behavior. The parabolic law form of the examined model has not been studied, and the obtained results have not been reported. [ABSTRACT FROM AUTHOR]

We have extracted some soliton solutions of the fractional longitudinal wave equation with the M-truncated derivative (M-LWE), which emerges in a magneto electro-elastic circular rod. To obtain new results of this model, the unified Riccati equation expansion and new Kudryashov methods have been utilized for the first time. The presented methods have been productively implemented to the considered model. With the help of these two methods, new soliton waves of the M-LWE have been obtained successfully. For a better understanding of the subject and analysis of the results, 3D, contour, and 2D graphs of some soliton solutions have been presented. The interesting part of our work is that both methods, named unified Riccati equation expansion and the new Kudryashov methods have successfully been applied for the first time to get new soliton solutions of M-LWE. [ABSTRACT FROM AUTHOR]

Because the importance of the optical wave propagation in fibers, we seek for the optical travelling wave solutions and effect of the third-order dispersion parameter for the extended nonlinear Schrödinger equation (NLSE) which is used to describe the femtosecond(fs) pulse propagation in optical fiber. We have used the modified F-expansion method because it is effective, sufficient and offers more solutions for this kind of problems. First, we obtain the nonlinear ordinary differential form (NODE) by using the wave transformation on the investigated extended nonlinear Schrödinger equation. Then, we propose the modified F-expansion method to get solution of the equation as the NODE form, and by calculating the balancing constant over the NODE form. By substituting the proposed solution function and its derivatives in the NODE form, we obtain an algebraic equation system over this NODE. With the solution of this system, we obtain the appropriate solution sets for the undefined parameters, and then, using the appropriate sets, the proposed solution function, the F-expansion solution functions, and the wave transform, together, we obtain the solution functions of the investigated problem. In order to contribute to the physical interpretation of the problem, 3D, 2D and contour graphs of the obtained solution functions were plotted and interpreted. The problem has not been examined by considering two different situations with the effect of third order dispersion parameter as in this study, before. In this respect, the results obtained in the study are new, and it is believed that they will contribute to the studies in this field. [ABSTRACT FROM AUTHOR]

In this paper, some analytical solutions for a model of dual-core optical fibers governed by a system of coupled non-linear Schrödinger equations (NLSEs) and the effect of the coefficient of the group velocity dispersion term on the considered model are investigated. The group velocity dispersion (GVD) has a important role in the optical wave propagation. The enhanced modified extended tanh expansion method (eMETEM) is successfully implemented to the governing model. The NLSE system is turned into a nonlinear ordinary differential equation (NLODE) via appropriate wave transformations. Supposing that the NLODE has solutions in the form suggested by the method and utilizing the enhanced solutions of the Riccati equation, we gain a nonlinear system of algebraic equations. The solutions of the governing model are obtained after solving the system of algebraic equations. 2D, 3D and contour illustrative figures for the physical interpretation of the attained solutions are presented. Besides, the result of the investigation, which is related to the effect of the coefficient of the group velocity dispersion term, is presented by supporting the various graphical scheme. [ABSTRACT FROM AUTHOR]

This article investigates the optical soliton solutions of the time-fractional Biswas–Arshed (BA) equation, which is a new model for soliton transmission through optical fibers where the eigen-phase modulation is negligible and thus removed. We have studied both models including M-truncated or beta derivative operators. Firstly, the time-fractional BA equations have been transformed into a nonlinear ordinary differential equation using appropriate wave transformations. The singular, singular-periodic, and dark soliton solutions have been derived using the extended rational sine–cosine and sinh–cosh techniques have been applied and the existing conditions for the obtained solutions have been introduced. Utilizing a computer algebraic system, we have verified that all of the derived solutions satisfy the fractional Biswas–Arshed equation. Additionally, we have compared the results for the beta and M-truncated derivatives and have examined how the equation's parameters affect the amplitude of the solitons in 2D and 3D graphical demonstrations. The attained solutions may aid in the comprehension of wave propagation in optical fibers and may contribute to the telecommunication sector. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated the perturbed Chen–Lee–Liu equation which describes the pulse propagation in the optical fibers, under the impact of the inter-modal dispersion, self-steepening and nonlinear dispersion terms. By using the enhanced modified extended tanh expansion method, bright, singular, periodic singular and periodic bright solitons have been obtained and the effects of the coefficients of the inter-modal dispersion, self-steepening and nonlinear dispersion terms on the soliton's dynamics have been examined in each case. In this respect, the review in the article has not been studied and reported before. The computations throughout this paper have been fulfilled by Maple and also the graphical simulations are demonstrated via Matlab. [ABSTRACT FROM AUTHOR]

In this study, we have focused on finding soliton solutions of the cubic–quartic Fokas–Lenells equation, which models the nonlinear pulse transmission through optical fiber, is a pretty new and updated model. The main motivation of this study is to produce new solutions with previously unused methods for data transmission models in fiber optic cables together with the developing technology, which has been used very frequently today. We have used three different efficient analytical methods, namely, the Sinh–Gordon expansion method, enhanced modified extended tanh expansion method and unified Riccati equation expansion method. By modifying our proposed method and using it effectively, we have obtained much more optical solutions. We have supported the results with the 3D surface, 2D and contour plots of the soliton solutions, such as singular, periodic, periodic-singular, dark and M-shaped solitons. The originality of the method we propose is that it has never been used before. With the innovation of the method, we have obtained M-shaped solitons, which are very rarely obtainable in soliton waves. On the other hand, enhanced modified extended tanh expansion method have provided us more extra solutions. As the last and most important part, in order to examine physical behaviors, we have investigated the effect of the coefficient of the fourth order dispersion parameter on wave propagation by presenting the graphical representation. [ABSTRACT FROM AUTHOR]

In this work, we aim to derive various soliton solutions to the Wazwaz–Benjamin–Bona–Mahony equation with conformable and M-truncated derivatives. The considered equation models long waves in the ocean engineering field. Unified Riccati equation expansion and Kudryashov auxiliary equation methods are used to the model, and so, kink, singular, and periodic-singular soliton solutions are successfully obtained. It is also reported on the constraint conditions that assure the validity of novel wave forms. By choosing appropriate parameters, numerical simulations of the obtained results are depicted by using two- and three-dimensional plots and the comparative results between the solutions for the conformable and M-truncated derivative are shown in two-dimensional graphs for various orders α , β . Moreover, the effects of the parameters in the obtained solutions are shown. The methods might be useful for obtaining the analytical solutions of many physical phenomena in nature since they are effective, robust, and easily applicable. Finally, this study contributes to extract both various solutions to the literature and to investigate wave behavior while the parameters change. [ABSTRACT FROM AUTHOR]

In this paper, we have successfully extracted many analytic solutions for the (1+2)-dimensional Chiral non-linear Schrödinger equation (NLSE) by the enhanced modified extended tanh expansion method (eMETEM). The considered method is a recently enhanced version of the classical modified extended tanh expansion method. So, we have successfully extracted the abundant solutions of the (1+2)-dimensional Chiral NLSE. Using a computer algebra system program, we have verified that all derived solutions satisfy the Chiral NLSE. The plots of some solutions are demonstrated to explain the dynamics of the solutions. It is expected that the results of the paper might be helpful for future works in traveling wave theory. [ABSTRACT FROM AUTHOR]

The phenolic compounds naturally found in vinegar composition have many positive effects on human health. In this research, it was aimed to investigate the effect of adding different amounts of oak chips during the fermentation stage on some physicochemical properties, total phenolic compounds, antioxidant capacity and individual phenolic compounds of grape vinegar. Acetic acid fermentation was carried out by adding oak chips in the amount of 0, 5, 10, 15, 20 g/L to the samples whose alcohol fermentation was completed. In vinegar samples, it was determined that the amount of phenolic compound (1328.96–1782.29 mg GAE/L), antioxidant activity determined by ABTS and DPPH method (1753.50–3258.50 mgTE/L and 199.17–727.78 mg TE/L) increased in parallel with the increase in the amount of oak chips. Ferulic acid and vanillic acid which is individual phenolic compounds, increased depending on raise in the amount of oak chips. In addition, it was determined that there was a significant increase in the amount of gallic acid in vinegar samples compared to wine. This study has shown that the use of oak chips in the acetification stage can save time and can be an alternative to the maturation process using oak barrels. [ABSTRACT FROM AUTHOR]

This paper presents an investigation of soliton solutions for the perturbed Fokas-Lenells (pFL) equation, which has a vital role in optics, using Sardar sub-equation method. The equation models the propagation of ultrashort light pulses in optical fibers. Using appropriate wave transformation, the pFL equation is reduced to a nonlinear ordinary differential equation (NLODE). The solutions of this NLODE equation are assumed to be in the suggested form by the Sardar sub-equation method. Hence, an algebraic equation system is obtained by substituting the trial solution and their necessary derivatives into the NLODE. After finding the unknowns in the system, the soliton solutions of the perturbed Fokas-Lenells equation are extracted. The method produces various kinds of solitons such as dark, periodic, singular periodic, combined bright-dark. To show physical representations of the solitons, 2D, 3D and contour plots of the solutions are demonstrated via computer algebraic systems. It is expected that derived solutions may be useful for future works in various fields of science, especially optics and so, it may contribute to the optic fiber industry. [ABSTRACT FROM AUTHOR]

This paper carries out the analytical optical soliton solutions of perturbed Radhakrishnan–Kundu–Lakshmanan (pRKL) equation with Kerr law nonlinearity using an efficient modified extended tanh expansion method, enhanced with the new Riccati solutions (eMETEM). In this study, we have established robust solutions for the pRKL by using the eMETEM method for the first time. We have focused to construct the effective scheme for the solution of governing model. Bright, dark, combined bright-dark, singular, multiple singular, flat kink-like, breather-like, periodic, different periodic optical solitons have been successfully obtained and confirmed with the help of Maple and Matlab symbolic computation packages. The physical properties of the data have been discussed and presented in 3D, 2D and contour graphics. The results have also been interpreted in the relevant sections. [ABSTRACT FROM AUTHOR]

Some new optical solitons find for the Kudryashov equation (KE) in this study. These solutions are in the form of dark, bright, singular, singular-dark solitons and other solutions with certain conditions. These new solutions may be applied in the demonstration of Kudryashov equation in some better way. Modified integration method, the extended Sinh-Gordon equation expansion method (ShGEEM) is utilized to secure the aforesaid solutions. The results are also verified with the use of Mathematica symbolic programming software. These optical solitons suggest that this method is effective and straight forward compared to other methods and the results are reliable. The obtained solutions are very helpful in the field of optical fibers. [ABSTRACT FROM AUTHOR]

In this study, we consider a class of nonlinear fractional difference equations following form where t ∈ Nt0+1−α and Δα denotes the Riemann-Liouville fractional difference operator of order α. Using the generalized Riccati function, we obtain some oscillation criteria. Finally, we give some illustrative examples. MSC 2010: Primary 26A33; Secondary 34A08, 39A21, 39A10 [ABSTRACT FROM AUTHOR]

In this study, the drying kinetics and modeling of enriched couscous with two different compositions (A and B) were carried out by using packed bed (60 and 80 °C) and microwave (180 and 360 W) drying techniques. Seven drying models were used to determine the best fitting of experimental data. Moreover, the effects of drying methods and parameters on color, yield and sensory attributes of enriched couscous were evaluated. It was found that microwave intensity increment is more effective on drying rate and drying time in contrast to the increment of drying air temperature in the packed bed drying. The free moisture contents of the enriched couscous decreased with time. The effective moisture diffusivities of enriched couscous produced with composition A and B were between 0.93 × 10−8 to 1.68 × 10−8 and 0.86 × 10−8 to 1.42 × 10−8 m2 s−1, respectively. Midilli and others model for the packed bed and microwave drying was observed to be the most suitable for the experimental data with the highest values of R2, and the lowest values of RMSE, χ2 and RSS. [ABSTRACT FROM AUTHOR]

In this study, effects of different tea concentrations and extraction durations on some characteristics of tea liqueurs were investigated. Total phenolics of tea liqueurs produced with different tea ratio and extraction duration were determined as 1496.8–4796.2 mgGAE/L. Caffeine was the major compound in all liqueur samples. Among phenolic compounds, gallic acid was the major phenolic and it was followed by epigallocatechin. The liqueurs with 7.5% tea ratio and 15–30 days extraction durations had the greatest total catechin contents. Sensory analyzes revealed that the liqueurs produced with 5% tea ratio and 15 and 30 day extractions were the most favourable samples. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with numerical methods to solve stochastic differential equations (SDEs), namely the Euler-Maruyama (EM) and Milstein methods. These methods are based on the truncated Ito-Taylor expansion. In our study we deal with a nonlinear SDE. We approximate to numerical solution using Monte Carlo simulation for each method. Also exact solution is obtained from Ito's formula. To show the effectiveness of the numerical methods, approximation solutions are compared with exact solution for different sample paths. And finally the results of numerical experiments are supported with graphs and error tables. [ABSTRACT FROM AUTHOR]

Couscous is produced traditionally by agglomeration of Triticum durum semolina with water. The aims of this study were: to produce couscous-like product by substitution of semolina with bulgur by-product (undersize bulgur); to find optimum quantity of bulgur flour and processing conditions. In order to determine the optimum processing parameters and recipes; 0, 25 and 50% of bulgur containing couscous-like samples were prepared. The color, yield, sensory properties, total phenol and flavonoid contents, bulk density, protein and ash content, texture properties were determined. Two different types of dryer e.g. packed bed and microwave were used. Optimum parameters were predicted as 50% of bulgur flour for packed bed (60 °C) and microwave (180 W) drying with 50% (w/w) of water according to yields, color (L*, a*, b*) values and sensory properties (color, odor, general appearance). For packed bed drying at 60 °C yields were 54.28 ± 3.78, 47.70 ± 1.73 and 52.57 ± 7.04% for 0, 25 and 50% bulgur flour containing samples, respectively. Lightness (L*) values of couscous-like samples were decreased with increasing the quantity of bulgur flour after both drying processes. Results of sensory analysis revealed that couscous-like bulgur were more preferable for consumers. [ABSTRACT FROM AUTHOR]

Color (CIE b*; yellowness) is an important parameter for bulgur quality. Color of bulgur is mainly due to natural pigments (carotenoids) that are present at different levels in wheat. In order to increase the customer acceptability, the producers try to obtain yellowish color in bulgur. In this study, two different tempering methods (spray and steam) were used before sun and UV- light polishing applications. Sun and UV-light were applied to tempered bulgur for 12, 24, 36, 48, 60 and 72 h. Moisture content (%, d.b.), ash content (%, d.b.), protein content (%, d.b.), total carotenoid content in terms of lutein equivalent (TCC) and color values (CIE L*; lightness, CIE b*; yellowness, CIE a*; redness and CIE YI; yellowness index) were determined. It was found that UV-light was more effective ( P < 0.05) on the CIE L* and CIE b* values compared to sunlight. Both tempering methods were significantly ( P < 0.05) increased the CIE L*, CIE b* and CIE YI values. Steam tempering has a significant effect ( P < 0.05) on the CIE b* values as well as UV and time of UV exposure. The highest value of TCC i.e. 6.31 μg/g was obtained by using spray tempering and UV-light exposure. As a conclusion, as proposed methods steam tempering and UV-light have an obvious positive effect on the color of bulgur. [ABSTRACT FROM AUTHOR]

The present paper aims to deal with a new iterative method to find a common solution of a generalized equilibrium problem, a variational inequality problem and a hierarchical fixed point problem for a sequence of nearly nonexpansive mappings. It is proved that the proposed method converges strongly to a common solution of above problems under some assumptions. The results here improve and extend some recent corresponding results by many other authors. [ABSTRACT FROM AUTHOR]

Effect of soaking time (20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320, 340, 360, 380, 400, 420, 440, 460, 480 and 500 min) and temperature (20, 30, 40, 50, 60, 70, 87, 92 and 97°C) together with ultrasound application (25 kHz 100 W and 25 kHz 300 W) on texture of chickpea was investigated. Soaking time, temperature, application of ultrasounds and power of ultrasounds had significant effect ( P < 0.05) on texture of chickpea. An Asymptotic first order texture model was successfully fitted to correlate texture of chickpea with soaking time and temperature. Texture model rate constant (k) increased from 1.68 × 10 to 19.20 × 10 s for a temperature change from 20 to 97°C without and with 25 kHz 100 W, 25 kHz 300 W ultrasound treatments. Average gelatinization temperature of chickpea using the model was found to be 60 ± 1°C. Activation energy (E) values of chickpea for below and above gelatinization temperature were found to be 26.49 and 9.73 kJ mol, respectively. Time to reach equilibrium texture level (t) of soaked chickpeas decreased from 941 to 82 min with increase of temperature from 20 to 97°C ultrasounds of 25 kHz 100 W and 25 kHz 300 W. In the food industry, chickpea is pre-processed (soaked and cooked) to produce humus, canned products and blended powder products. Ultrasonic treatments can be applied to soften and inturn decrease the cooking time of the chickpeas. [ABSTRACT FROM AUTHOR]